The Sergeant's badge seen close up does not appear to match the one always seen in the opening and closing credits.
After firing his gun at a burglary suspect, Sgt Friday calls in the incident to the station. He reports the suspect's profile and then says "suspect headed west on Vermont". That would be impossible since Vermont is a north-south street.
The captain takes Friday's badge, stating he was given it the day he became a police officer. Friday has since been promoted to sergeant, like the badge shown in the credits, he would have one like it, not his original badge.
After finding the slug one of the shooting team detectives tells Friday that he had the geography figured almost to the inch. He most likely meant geometry, which deals with angles, lines and direction whereas geography almost exclusively deals with terrain features of the Earth.